Question

Which of the soultion is set to the equation (x-2)² =25

Answer 1

To solve (x - 2)² = 25, we find two solutions by taking the square root of both sides. The solutions are x = 7 and x = -3, by adding and subtracting the root from the constant term.

Step-by-step explanation:

To solve the equation (x - 2)² = 25, we can take the square root of both sides of the equation. Taking the square root of a square eliminates the exponent, but remember that there will be both a positive and negative root. Therefore, the equation will have two solutions:

• x - 2 = 5
• x - 2 = -5

Solving each equation for x gives:

• x = 2 + 5
• x = 2 - 5

So the two solutions are:

• x = 7
• x = -3

These are the solutions to the given equation, obtained by recognizing that the left side is a perfect square.